Question

use f(x)=lim_{h→0} \frac{f(x + h)-f(x)}{h} to find the derivative at x for the given function. s(x)=7x + 8 s(x)=□

Explanation:

Step1: Find s(x + h)

Substitute x + h into s(x): s(x + h)=7(x + h)+8 = 7x+7h + 8

Step2: Calculate s(x + h)-s(x)

s(x + h)-s(x)=(7x + 7h+8)-(7x + 8)=7h

Step3: Calculate \(\frac{s(x + h)-s(x)}{h}\)

\(\frac{s(x + h)-s(x)}{h}=\frac{7h}{h}=7\)

Step4: Find the limit as h→0

\(s^{\prime}(x)=\lim_{h
ightarrow0}\frac{s(x + h)-s(x)}{h}=\lim_{h
ightarrow0}7 = 7\)

Answer:

7